Dyson's transform

Dyson's transform is a fundamental technique in additive number theory for transforming a pair of integer sequences into another pair of integer sequences. It was developed by Freeman Dyson as part of his proof of Mann's theorem on the Schnirelmann density of sumsets, is used to prove such fundamental results of additive number theory as the Cauchy–Davenport theorem on the size of restricted sumsets, and was used by Olivier Ramaré in his work (related to the Goldbach conjecture) that proved that every even integer is the sum of at most 6 prime numbers. The term Dyson's transform for this technique is used by Ramaré. Halberstam and Roth call it the τ-transformation.